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C₂×#12741 #493536

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

3284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 4 generators on 34 points:

(1,2);(3,4)(5,14,16,10)(6,9)(7,21)(8,12)(11,18)(13,19)(15,27,32,22)(17,26,31,29)(20,23)(24,33)(25,30,28,34);(4,9)(6,18)(7,19)(10,22)(11,13)(12,23)(14,27)(15,30)(17,31)(20,33)(21,24)(25,26)(28,29)(32,34);(3,5)(4,10)(6,15)(7,17)(8,16)(9,22)(11,25)(12,14)(13,26)(18,30)(19,31)(20,32)(21,29)(23,27)(24,28)(33,34)

Conjugacy classes & character table

80 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 400732);